This strikes me as a non-sequitur. Everybody uses a calculator. The question is, how do you know what to punch into the calculator? And this is where algebra and/or memorized formulas come in.
Perhaps he meant a symbolic calculator? Otherwise, yeah, I was confused by that too.
(I suppose he probably feels he is generally able to figure out what to punch in without having to write down "x"es. Which, you know, good for him. I don’t take any issue with “x” training, though; that’s in the part of algebra I think people would do well to be comfortable with.)
Instead of “scientific calculator”, I’m guessing he means “financial calculator” or “business calculator” such as this common one: HP-12C - Wikipedia
I saw that HP-12C on every mortgage analyst’s desk in the 1990s – especially before Microsoft Excel became popular.
With that device, the user thinks in terms of “what numbers he already knows” (principal, years, etc) and then what he wants to figure out (the interest rate) and the calculator will have obvious functions for that. It will also calculate loan payments, NPV, etc.
One definitely does not need to know any algebra to use that calculator.
On the other hand, do most surveyors know (or need to know) trigonometry when using a total station? That, I don’t know.
Yes, that was pretty much what I meant by we need a better way of teaching mathematics.
You know, I find that breathtakingly … well, obtuse, on a board with the motto “Fighting Ignorance …”
We should just give up? Not look for a better way?
We should just give up on the kids? Tell them, what? You don’t need to manage money. You don’t need to grasp the fundamentals of logical thought. You’ll never need to modify a recipe for more servings, and use honey instead of sugar.
Part of raising kids is teaching them to do things they see no need for, and things they don’t particularly want to do, because having these skills will benefit them in the real world.
I strongly disagree. Math history within content-based courses can help cast mathematics as a human endeavor as opposed to a series of formulas to memorize.
In cases where we have a good knowledge of the history, it can make it easier for students to grasp the underlying concepts, precisely because the creators’ have been humanized.
This works best in calculus, since we have a strong record of the creation and of the mistakes made. Students are willing to put up with two sets of conflicting notation once they become aware of the reasons behind it. A subset of students will inevitably misremember the product rule. Pointing out that Leibniz got it wrong originally too and how to fix it makes it easier to remember the actual formula. (Not least of all since students are more likely to remember that the formula (fg)’ = f’g’ is flat out wrong.)
I think the problem goes all of the way back to the Greeks. We have this worship of abstract mathematics like it is some great proof of intelligence and students are supposed to prove to the teacher that they are smart. But the Greeks did not have electricity. But now we live in a society that depends on electricity.
How many kids are not taught squat about electricity.
We could start with Ohm’s Law and use that to begin algebra and kids would see that the math has something to do with REALITY.
Even make use of cheap computer tablets.
https://play.google.com/store/apps/details?id=com.everycircuit&hl=en
That is a cool program. I am running it on my Nexus 7.
And kindergarten kids should have abacuses so they can feel the numbers. Get out of abstract reality.
psik
Seeing the formula “V = IR” won’t motivate algebra for any kids beyond what we have now. Kids are already well aware that multiplication comes up in physics…
(Playing around with the program you link to could be pedagogically useful, though. But, of course, there are kids who are no more interested in circuit design than in algebra…)
What I mean is, it’s the playing around that matters, and not the trappings.
“Math is connected to REALITY because math is used in physics” is not, I would think, a message that anyone is unaware of. Saying “Look, math is useful because it can be used to describe and analyze the relationship between resistance, voltage, and current in circuit design. Here, take a hold of this ohmmeter…” will only make the kids who presently dislike math also switch from neutral to dislike re: circuit analysis.
But “Math is a tractable and potentially fun activity because math is just what happens when you play around and think about puzzles, of pretty much any sort (whether they arise in ‘real life’ or a computer game or what have you)” is a message that could use more exposure. It couldn’t hope to captivate everyone, but it could swell the numbers a bit.
I really like that idea.
What s/he said.
Kept meaning to get back to this. Here are some math topics which have proven utterly critical to programming projects I’ve worked on either in my fairly short career as a programmer or as a hobby:
Polygonal 3D graphics: algebra, trigonometry, linear algebra, projective spaces, quaternions
Ray traced 3D graphics: all of the above, advanced algebra (line/surface intersections, high-degree root-finding, etc.)
Fractal rendering: complex numbers
Error-correcting file splitter: linear algebra (matrix inversion, etc.), finite (Galois) fields
Inertial navigation unit: Recursive (Kalman) filters, trigonometry
Fast arbitrary-precision arithmetic library (million digits of pi, etc.): Fourier transforms, convolution
Software-defined radio decoding: Frequency domain math, complex numbers, trigonometry, filtering
Benchmark suite: statistics (confidence calculation, outlier rejection algorithms, etc.)
Physics simulation: Numeric differential equations, calculus
Various control units: control theory, calculus, filtering
Databases (SQL): Set theory
Functional languages: lambda calculus
This is just the handful of projects that immediately came to mind. Of course, I’m ignoring common programming stuff like Boolean logic (De Morgan’s laws, etc.). And I still feel like I’m totally math-limited, despite taking about 7 quarters of math in school.
About the only math I really don’t see much use for is continuous differential equations, mostly because most interesting equations don’t actually have solutions. A course on numeric diffeqs would have been more useful. That said, continuous diffeqs at least gave me an understanding of the basic concept and a basis for learning more.
A Political Science professor wants to do away with Algebra.
Please have the professor provide an example of a triple blind study in which this thesis has been studied in identical environments with identical subjects.
Include the statistical raw data and calculation methodology used to determine outcomes.
Since he is a Political Science professor he should be able to comply with the rigors of the scientific process.
Thank you.
Your friend,
STEM
Just thought I would throw this in for fun – and another reason to learn algebra.
Anyone remember a Philip K Dick story called The Pre-Persons? In it, the US Congress writes a law making abortion legal up to the point the soul enters the body. The law defines that point as the time when a person learns algebra. 
Algebra – it can save your life!
How do you teach DeMorgan’s theorem, or any logic, without algebra? How do you do programming without a basic understanding of logic?
Sure, it’s POSSIBLE to study logic without using boolean algebra, but is it wise?
The main justification of teaching algebra is that we don’t want young kids ruling themselves out of later deciding to go into a science/math discipline. Algebra is necessary for any math/science discipline.
But it would be better to toss in some prob/stat, and skip conic sections. I mean, who needs conics? Is it cool? Sure. But it shouldn’t be a high school college-prep requirement.
I don’t follow you at all. I happened to know algebra before I learned logic, and learning algebra may have helped in that I had learned to think of symbols as formal and meaningless objects of manipulation–to be interpreted before and after but not during the manipulation. But that could easily have gone the other way. I could have learned all that from logic, then applied all that to my later learning of algebra, had things gone in that order.
Is there some other aspect of algebra you think is necessary to the learning of logic?
You studied logic without using boolean algebra? Without understanding the associativity and commutativity properties of logical expressions? (or making logical expressions, for that matter, without using algebraic expressions?)
Sure, we don’t need to know how to factor a quadratic. But we do need to know the elements of algebra (variable substitution, etc).
As I said: sure you can teach logic without using algebraic expressions or manipulation, for example, just using truth tables. But can you get far, and even if you can, why do it the hard way?
I’ve never used statistics or ratios or proportions in my life, nor chemistry or physics or history.
Anyways I partially agree, it would be best to have a greater and earlier specialization, like in japan.
on the other hand, about algebra it should be on its way to dying,with a faster and more conceptual approach to the matter, and leave the calculations to machines, remember that 50 years ago you were required to know how to take square roots of big (5 digits) numbers before high school; know you know what is a square root and give qualitatives statements but giving the exact number is deemed dry and uninteresting, because we just use the calculator.
I think you two might just be using Algebra differently. I think Frylock (and I don’t presume to speak for him, just what I infer from his statement), is just saying that you could just as easily introduce boolean algebra in a logic class and later teach kids that numerical algebra (for lack of a better term) is similar, rather than the other way around like we do now. In other words, you’re using algebra to mean a specific form of symbol manipulation that can collectively be called algebra and Frylock is using it to refer to the literal math class that is nowadays referred to as simply “algebra.”
There are too many problems with early specialization, IMO. I mean, most college kids already don’t know what they want to major in. Now you want to lock them into a track at 11? I mean, sure, by the time I was 10 I knew I wanted to program or work with computers in some capacity, but for most people? Most people either didn’t know or were still in the “astronaut/fireman/policeman” mindset. I’m not saying this to paint myself as superior. In many ways I envy the people who drifted between not knowing whether they wanted to be an actor, a writer, or a scientist of some stripe.
I’m not sure I’m comfortable making kids, or even young teenagers choose and stick with a path so early. I do think there should be methods for doing so should you so choose, but I don’t think we should go “okay, you’re going into high school now, sure hope you’ve thought long and hard about what you want to commit your life to doing!”
I will admit though, I’m not that clear enough on Japan’s education system as you refer to it. I thought they were less about specialization in certain subjects, and more about segregating the “smart” from the “dumb” by standardized tests like Germany and France. Though in Japan I guess there is a small added stigma of the top of the top are going to be doctors no matter what. I definitely oppose segregating students based on test scores that early.
sorry, i know a couple of japanese with p.h.d that are like 18 years old or something, I may have generalized incorrectly.
If you’ve voted or invested, you’ve referred to history and statistics, or done so badly.
If you have cooked, you have used chemistry.
If you have cooked from a recipe, you have used ratios. (Or served six people with enough food for four ..).
If you have down shifted and/or accelerated going into a curve, you have used physics.
If you soaked beans in salted water, you’ve used both.
If you’ve done algebra with a calculator, please tell me how; I always set up the equations in a spreadsheet, screw them up, and then do it by hand.
Algebra is the first step in learning to solve problems scientifically.
If a, then b != if b, then a is fundamental to logic.
Dimensional analysis, a form of algebra, is fundamental to understanding science and the physical world.
The more I think about it, the more I believe that dissing algebra is part of a Conspiracy to take power, in the form of understanding, from the Common Person.